Constitution? Magna Carta?
Ooh, a chartist!
Magna Carta isn't a written constitution, though it does contain elements that would later be incorporated into the constitution of the United States and many of their state constitutions.
We don't have a written constitution. We have several documents and treaties that together form our constitution: magna carta, the acts of settlement, the Act of Union and the parliamentary Bill of Rights, which several of our erstwhile representatives have recently tried to resurrect in order to avoid prosecution for fiddling their expenses. Our constitution is largely statute-based, which is why it's often referred to as unwritten.
The big problem is that people don't know about this. Ask the average person on the street what they think about magna carta and they'll ask if it's that classical music record label *if you're lucky*. They might think it's a spanish football team. Without that knowledge of how our government was established, it is impossible to prevent the government from going beyond the bounds set for it by those documents. The Bill of Rights is a good example, as it guarantees certain things (including the right to own guns as long as you aren't a catholic, and the limitation on unfair taxation without legislation enacting that taxation - bye bye nearly every non-criminal penalty charge in existence!) that have subsequently been overridden by successive governments. The problem is that the Bill of Rights establishes Parliament, and isn't an Act of Parliament but a treaty. Overriding it removed the constitutional basis for Parliament to legislate, which means that current moves to use the concept of Parliamentary Privilege as established in the Bill of Rights means that either the Bill of Rights is supreme, in which case nearly every piece of legislation for the past 100-odd years is invalidated, or that the Bill of Rights must be struck down, in which case every piece of legislation since 1668 is invalid.
As for the US Senate, as per their constitution that body was meant to represent the States, not the population as a whole. The house of representatives represents the people. The Senate was meant to act as a brake on populist legislation, a body of oversight similar to the House of Lords (probably the only marginally functional part of our own legislature left) and was meant to consider bills produced by the House and re-write them, or block them, before they went to be signed by the president. This is why their constitution includes a requirement for the senate and house bills on any subject to be worded identically before they can be signed into law.
A constitutional amendment requires two thirds of both the house and the senate, but even that would just call a constitutional convention. Constitutional convention then requires a two-thirds majority of all the states.
You see the constitution governed the Union of the States, not the sun-total of the population, which is why it was originally so small. The individual states governed their own populations as they saw fit, as long as they didn't breach the articles and amendments of the Bill of Rights, which restricted the state to the smallest possible functional level by intention. The Federal government was meant to function as primarily an arbiter of the collective position of the States towards common problems and international issues and so in the constitution its powers and roll were very strictly limited. The expansion of the role of the federal government since the 1890s has resulted in a situation where the federal government has already broken past its constitutional limits many times, which is why you often hear references to the constitution being a "living document", not to mention a great deal of resentment amongst the elected representatives of the people and the states that a document written by a bunch of "dead old white guys" still has enough potency to limit their aspirations for absolute power.
Our "unwritten constitution" has lost that potency. Most criticism of the US from our side of the atlantic seems to be blinkered by an inability to understand how little freedom we have left compared to them, or perhaps a profound case of denial at just how restricted our lives are. Yes, their government is moronic these days, and they are pushy and loud, but they still have their constitutionally guaranteed rights. What do we have? Mandelson's muppetry and Ms Hillier's ID cards. I personally break the law several times a day doing things that are still considered to be inviolable rights in any functional society, but which have been rendered illegal here simply because the government of the day decided that it could do so. Criticism of America for problems that are even worse here smacks of a little bit of projection, I reckon, especially as we have no mechanism for restricting the activities of the state when it reaches too far. Think about that next time you're criticising the US. They may not exercise it all the time but they have that option to declare acts of the state unconstitutional. Do we? No. Even the much vaunted human rights act is filled with so many caveats and contradictions to make it useless for anything other than forcing people to comply with whatever positivist "rights" are the current politically correct whim.
Face it. We're fucked.